Dilations of some VH-spaces operator valued invariant kernels

DOI10.1007/s00020-012-2009-1zbMath1279.47023OpenAlexW2116964728MaRDI QIDQ1946573

Aurelian Gheondea

Publication date: 15 April 2013

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/11693/21207

zbMATH Keywords

\(*\)-representationdilationreproducing kernelKolmogorov decompositioncompletely positive map\(*\)-semigroupinvariant kerneladmissible spaceVH-space\(B^*\)-algebraHermitian kernel, positive semidefinite kernel

Mathematics Subject Classification ID

Dilations, extensions, compressions of linear operators (47A20) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89) Positive definite functions on groups, semigroups, etc. (43A35)

Related Items (4)

Representations of \(\ast\)-semigroups associated to invariant kernels with values adjointable operators ⋮ Representations of \(*\)-semigroups associated to invariant kernels with values continuously adjointable operators ⋮ Invariant weakly positive semidefinite kernels with values in topologically ordered $*$-spaces ⋮ Automatic boundedness of adjointable operators on barreled VH-spaces

Cites Work

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• LOCALLY C*-ALGEBRA
• Theory of Reproducing Kernels
• Positive Functions on C ∗ -Algebras
• Representations of Hermitian kernels by means of Krein spaces. II. Invariant kernels

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